1. Field of the Invention
This invention relates to the lithography technology. More particularly, this invention relates to a method of predicting photoresist patterns defined by a plurality of photomask patterns, a method of analyzing the measurement data of real photoresist patterns defined by a plurality of patterns on an existing photomask, and a simulation of photoresist patterns defined by a plurality of photomask patterns.
2. Description of the Related Art
As the linewidth of IC process is much reduced, optical proximity correction (OPC) is usually required in the design of a photomask. To check the effects of OPC, photomask patterns with OPC have to be verified based on the prediction of photoresist patterns defined thereby, which is conventionally based on a simulation of the exposure intensity distribution at the photoresist layer. By setting a threshold intensity, predicted photoresist patterns are obtained from the distribution. According to the photoresist patterns predicted, further OPC is done to further modify the photomask patterns so that the later predicted photoresist patterns are closer to those required by the IC process.
When only the setting of the exposure optical system is considered, the exposure intensity at a position of the photoresist layer can be calculated by numerical integration of the following Hopkins integral as disclosed in U.S. Pat. No. 7,079,223:I0({right arrow over (r)})=∫∫∫∫{right arrow over (dr)}′{right arrow over (dr)}″h({right arrow over (r)}−{right arrow over (r)}′)h*({right arrow over (r)}−{right arrow over (r)}″)j({right arrow over (r)}′−{right arrow over (r)}″)m({right arrow over (r)}′)m*({right arrow over (r)}″)  (1),wherein h is the lens impulse response function also known as the point spread function (PSF), j is the coherence function, m is the mask transmission function, “*” indicates the complex conjugate and “r” is the position of the image. I0({right arrow over (r)}) is the intensity of the aerial image at the position “{right arrow over (r)}”, and is also the basis of the physical optical kernel.
However, when aspects of the other photoresist exposure and chemical kinetics, such as the diffusion of the photoacid in the photoresist layer, are taken into account, a mathematical load kernel is usually used in the simulation to represent the effect of the photoresist chemical kinetics, because the photoresist chemical kinetics is very complex and is difficult to simulate by mathematical formulae satisfying chemical principles.
A traditional mathematical load kernel is a full Gaussian distribution function which is expressed as formula (2):
                                          1                                                            2                  ⁢                  π                                            ⁢              σ                                ·                      ⅇ                                                            -                                      r                    2                                                  /                2                            ⁢                                                          ⁢                              σ                2                                                    ,                            (        2        )            wherein σ is the standard deviation of the Gaussian function, as the only one parameter capable of modifying the shape of the kernel. However, since the proximity behaviors of patterns with different line widths and pitches are usually relatively different, it is difficult to fit all photoresist patterns of different pitches and linewidths with only one parameter. For example, photoresist patterns with a small critical dimension cannot be fitted well enough with a load kernel as a full Gaussian distribution function with only one parameter (σ).